The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.
"Stability of Impulsive Differential Systems." Abstr. Appl. Anal. 2013 (SI28) 1 - 11, 2013. https://doi.org/10.1155/2013/253647